Rotational Inertia is an integral part of any electric power system. Due to the increased use of power electronics-both to connect Renewable Energy Sources (RES) and as drives for electric motors-inertia levels are generally reduced and become time dependent. The same power electronic technologies can also be used to actively provide inertia to the power system, raising the question what effect changes in inertia has on power system stability, and how to best place devices providing virtual inertia. We propose an optimization program that answers these question, and analytically derive the sensitivities of transient frequency overshoot and damping ratio to inertia and damping. An example shows how damping ratio can be improved while transient frequency limits are respected.